Japanese Language Stack Exchange is a question and answer site for students, teachers, and linguists wanting to discuss the finer points of the Japanese language. It's 100% free, no registration required.

3 Answers
3

First, we can't make the blanket statement that 一緒で is always incorrect, only that it is incorrect in this particular case.

Let's start by identifying how に is used here. In the case of 一緒に, に works the same way as in expressions like きれいに ("neatly", "prettily") and 気軽に ("casually"): it turns the preceding word into an adverb and shows how the action is done.

Because the point of 一緒 in the sentence 一緒に行こう is to show how the action is done ("together" as opposed to, say, "separately"), it must be followed by に.

On the other hand, で, when following a quantity or a noun identifying a group, expresses the range of the subject (such as in 一人で, 二人で, みんなで, and 家族で) and shows how many people/things participated in the action. 一緒 is too vague to be used with で in this sense, because it does not specify a number or a precise grouping.

But there are cases when 一緒 can be followed by で. This typically indicates that the parties involved are in the same physical location, but they may not be performing the same action. (In these cases, the line between the particle で and the ～て form of だ gets blurry.)

この会社では、社員は一緒で昼食をとる。 At this company, the employees have lunch together. [Implying that some may start eating a little before others, but everyone has lunch in the same place and at roughly the same time.] (incorrect)

友達と一緒でよかった。 I'm glad I was with a friend.

子供と一緒で荷物が多いと大変です。 It's tough when you're with your kids and you have a lot of luggage.

一緒 could also indicate that two things are the same; in this case, 一緒で can be replaced with 一緒であって:

彼は母校が一緒で、子供のころは毎日遊んでいた。 He went to the same school as I did, and when we were kids we played every day.

This is only a speculation, but the etymology might be relevant. 一緒に derives from 一所に, which means 'at/to one place'. So the expression 一緒に行こう 'let's go together' is etymologically driven from 一所に行こう 'let's go to a single place'. In the latter, 一所 'a single place' is the destination, and hence you should use に instead of で. If that is just carried over to the usage of 一緒に, then it will make sense.